ABSTRACT The forecast for atmospheric and turbulence conditions above astronomical observatories is of interest to the astronomical community because it allows observations to be planned with maximum efficiency, a process called flexible scheduling. It can also be used to simulate long-term site testing to provide local information useful for the conception of focal and post-focal instrumentation. We have presented our forecasting tool in previous publications, but in this paper we focus on the importance of using local measurements to improve the predictive turbulence model and to better consider the local specificities of a given site, a process we call site learning. For this study, we use a local data base provided by the Calern Atmospheric Turbulence Station, which has been operational since 2015 at Calern Observatory. In addition, we use a set of several months of predictions to feed the turbulence model, taking into account daytime and nighttime conditions. This upgrade improves the quality of our forecasting by reducing the absolute bias between measurements and predictions from 25 to 50 per cent for each layer of the $C_n^2$, by 25 per cent for the seeing, and by 70 per cent for the isoplanatic angle.